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Even & Odd Functions Depending on a functions symmetry, it may be classified as even, or as odd. Depending on a functions symmetry, it may be classified as even, or as odd. Not every function is even or odd. Some are neither. Not every function is even or odd. Some are neither.

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Even Functions Even functions have symmetry about the y-axis. Even functions have symmetry about the y-axis. Everything to the left of the y-axis is exactly the same as everything to the right of the y-axis. Everything to the left of the y-axis is exactly the same as everything to the right of the y-axis.

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Examples of Even Functions

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Even Functions Another way to tell if a function is even is to create a table of values. Another way to tell if a function is even is to create a table of values. If opposite inputs give equal outputs, then the function is even. If opposite inputs give equal outputs, then the function is even. (Remember: E for equal, E for even) (Remember: E for equal, E for even)

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Even Functions Lets look at f(x) = x 2. Lets look at f(x) = x 2. Create a table of values using opposite inputs (x=1, x=-1 and x=2, x=-2). InputxOutput f(x) = x 2 1 1 2 = 1 (-1) 2 = 1 2 2 2 = 4 -2 (-2) 2 = 4 Opposite inputs (1, -1) produced outputs that were equal (1 and 1). Opposite inputs (2, -2) produced outputs that were equal (4 and 4).

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Odd Functions Odd functions have rotational symmetry. Odd functions have rotational symmetry. When you turn the graph upside down, it looks the exact same. When you turn the graph upside down, it looks the exact same.

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Examples of Odd Functions Right Side Up Rotated – upside down Even though the graph on the right has been turned upside down, the function still looks the same.

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Odd Functions Another way to tell if a function is odd is to create a table of values. Another way to tell if a function is odd is to create a table of values. If opposite inputs give opposite outputs, then the function is odd. If opposite inputs give opposite outputs, then the function is odd. (Remember: O for opposite, O for odd) (Remember: O for opposite, O for odd)

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Even Functions Lets look at f(x) = x 3. Lets look at f(x) = x 3. Create a table of values using opposite inputs (x=1, x=-1 and x=2, x=-2). InputxOutput f(x) = x 3 1 1 3 = 1 (-1) 3 = -1 2 2 3 = 8 -2 (-2) 3 = -8 Opposite inputs (1, -1) produced outputs that are opposite (1 and -1). Opposite inputs (2, -2) produced outputs that are opposite (8 and -8).

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Your turn… Tell whether the graphs or equations are odd or even or neither. Tell whether the graphs or equations are odd or even or neither.

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Even, odd, or neither?

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f(x) = x 3

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Even, odd, or neither? f(x) = x 2 + 4

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Even, odd, or neither? f(x) = x 3 – x 2

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Even, odd, or neither? f(x) = -x 3 + 2x

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Even, odd, or neither? f(x) = x 3 + 4x + 1

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Quiz Number your paper 1 to 13.

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Even, odd, or neither?

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f(x) = x 3 + 4x + 1

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Even, odd, or neither? f(x) = x 2 + 4

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Even, odd, or neither? f(x) = x 3

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Even, odd, or neither? f(x) = x 3 – x 2

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Even, odd, or neither? f(x) = -x 3 + 2x

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Do Now Graph both of these functions on the same graph from –2 ≤ x ≤ 2.

Do Now Graph both of these functions on the same graph from –2 ≤ x ≤ 2.

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